On the other hand, a block transmission framework is adopted for joint active device separation and device-RIS channel estimation. Specifically, each active device divides its \(B\) -bit message
into \(L\)  sub-messages [1]} and the length of the \(l\) -th sub-message is \(B_l\)  bits, as illustrated in Fig. REF . Then, active devices transmit their \(L\)  sub-messages sequently, which are jointly recovered at the BS. Noting that since each subblock \(l\)  contains \(K_a\)  recovered sub-messages, only an instance of the transmitted data can be obtained in each subblock. However, the ultimate goal of the BS is to recover the whole set of \(B\) -bit messages that were transmitted by all the active devices. To achieve this goal, a decoder for decoding binary messages among different subblocks of all the \(K_a\)  active devices is needed. For example, in [1]}, an outer tree-based decoder was adopted to stitch the decoded binary sequences across different subblocks (cf. Fig. REF ). Based on the recovered message, the BS can separate the active devices if they embed their identity (ID) information into the transmitted messages. Note that the inner decoder of URA is quite different from the conventional blind detection problem [3]}. First, the devices in URA share a common codebook, while the devices in blind detection may be assigned separate codebooks. Moreover, the receiver of URA neither knows the transmitted codewords, nor the number of transmitted codewords. In contrast, the blind detection generally has the knowledge of the number of transmitted codewords [3]}.
